How do I solve an Algebra word problem involving two variables?

Question

"Mrs. Sweeny is 7 times as old as her daughter. Eight years from now, she will be three times her daughter's age. How old are they now?"

I got D=7S, D+8=3(S+8), but I don't get the answer listed in the back of my summer review packet.

And a bonus question: How do I solve this problem using the quadratic forumla X^2/2-X/2=1. I don't ever remember doing the quadratic equation with fractions.

Thanks in advance.

Answer 1

well for the first one:

S = Mrs Sweeny
D = Daughter

s = 7d

(remember u have to add 8 years to both the daughter and mother's age!)

s+8 = 3(d+8)

(plug in the equation s = 7d)

(7d) + 8 = 3d + 24

4d = 16

d = 4

daughter is four, and mother is 7(4)= 28

in 8 years, mrs. sweeny will be 3 times as old as her daughter
check: 28 + 8 = 36

4 + 8 = 12, and 12 * 3 = 36!!! ta da~

for the 2nd question, oh is it (x^2)/2 - x/2 = 1!

ok, so yeah, common denominator, multiply all by 2 to get rid of fraction:

x^2 - x = 2

x^2 - 1x - 2 = 0 (find 2 numbers that multiply and equal -2....and add up to -1)

(x - 2)(x+1) = 0

x = 2, x = -1

:)

Answer 2

Your equations are wrong, assuming D=daughters age, and S=mrs sweeny's age:
mrs Sweeny is 7 times as old as her Daughter, so:
S=7D, and S+8=3(D+8)
Also, from the problem, I can't tell if she will be three times her daugther's age NOW, or in 8 years. So try it with S+8=3D

As for the quadratic, multiply both sides by two to get:
x^2 - x -2 = 0
a=1 b=-1 c=-2

Answer 3

well for the first one:

S = Mrs Sweeny
D = Daughter

s = 7d

(remember u have to add 8 years to both the daughter and mother's age!)

s+8 = 3(d+8)

(plug in the equation s = 7d)

(7d) + 8 = 3d + 24

4d = 16

d = 4

daughter is four, and mother is 7(4)= 28

in 8 years, mrs. sweeny will be 3 times as old as her daughter
check: 28 + 8 = 36

4 + 8 = 12, and 12 * 3 = 36!!! ta da~

for the 2nd question, oh is it (x^2)/2 - x/2 = 1!

ok, so yeah, common denominator:

x^2 - x = 2

x^2 - 1x - 2 = 0 (find 2 numbers that multiply and equal -2....and add up to -1)

(x - 2)(x+1) = 0

x = 2, x = -1

Answer 4

OK. If D=7S, then substitute 7S in your second equation. It'll look like this:

7S+8 = 3 (S+8)

Now simply the right side by multiplying both S and 8 by 3. You'll get this:

7S+8 = 3S + 24

Subtract 8 from both sides and you get:

7S = 3S + 16

Now, subtract 3S from both sides and you get:

4S = 16, so S = 4. That's not Mrs. Sweeney's age, that's her daugther's age. Mrs. Sweeney, who is seven times older, is 28.

You can check it by running through the second part of the equation. In eight years, the daughter will be 12 (s+8), and if Mrs. Sweeney is 28 now, she would be 36 in eight years. Is 36 three times older than 12? Yup.

For the quadratic equation, it looks like the equation is x squared over 2-x divided by 2 = 1. If that's the case, let's go:

Start by multiplying both sides by 2. That'll give you x squared divided by 2-x = 2.

Now multiply both sides by 2-x. That'll give you x squared = 2(2-x), or x squared = 4 - 2x

Now, add 2x to both sides and you get x squared + 2x = 4. If you then subtract 4 from both sides, you get x squared + 2x - 4 = 0. You should be able to apply the quadratic equation from there.

Answer 5

That's because D=7S is incorrect. Actually, S=7D (Sweeny is 7 times as old as the daughter.)

Answer 6

First off, S=7D
S+8=3D
The first eqn defines S in terms of D, so substitute it into the second, so the second will be all D's.
7D+8 = 3D
7D-3D = -8
D = -8/4
something isn't right